# Symbolic Algorithm for Solving SLAEs with Heptadiagonal Coefficient Matrices

## TL;DR

This paper introduces a symbolic algorithm specifically designed for solving systems of linear equations with heptadiagonal matrices, including a stability condition theorem, advancing computational methods for such structured matrices.

## Contribution

The paper presents a novel symbolic algorithm for heptadiagonal SLAEs and provides a proven stability condition, enhancing solution techniques for structured band matrices.

## Key findings

- Algorithm successfully solves heptadiagonal SLAEs
- Stability condition theorem established and proven
- Potential for improved computational efficiency

## Abstract

This paper presents a symbolic algorithm for solving band matrix systems of linear algebraic equations with heptadiagonal coefficient matrices. The algorithm is given in pseudocode. A theorem which gives the condition for the algorithm to be stable is formulated and proven.